An index to quantify an individual's scientific research output

(Taken from J. E. Hirsch, An index to quantify an individual's scientific research output, arXiv:physics/0508025)


A scientist has index h if h of her/his N papers have at least h citations each, and the other (N-h) papers have no more than h citations each. A high h-index is claimed to be a reliable indicator of high accomplishment but the converse is not necessarily always true.

Adopting a linear model h=m*n, the m-parameter gives the estimated value of the h-index after n years of publishing, assuming that papers of similar quality are produced at a steady rate.


Although the h-index is time-dependent (especially early in the scientific career), it can never decrease, only increase. The m-parameter may strongly fluctuate up and down and ceases to be useful if a scientist does not maintain the level of productivity, while the h-index remains useful as a measure of cumulative achievement at any time.

However, a direct comparison of the h-indices is only possible for two individuals with the same scientific age n. Using the m-parameter and the linear model above, the h-indices of two individuals can be adjusted to the same n, although this may be inaccurate.

Based on typical values for h and m, the following interpretation (with large error bars) is proposed:

h-index: (for faculty at major research universities)
(note the possible strong time-dependence of m during a person's career!)
(Taken from J. E. Hirsch, An index to quantify an individual's scientific research output, arXiv:physics/0508025)


E. Witten, h=110, m=3.89
S. Weinberg, h=88, m=1.76
P.G. deGennes, h=79, m=1.75
J.N. Bahcall, h=77, m=1.75
F. Wilczek, h=68, m=2.19
S.W. Hawking, h=62, m=1.59

Group of physics Nobel prize winners from the last 20 years:
average h=41 (standard deviation 15), median h=35
average m=1.14 ( 0.47) (49% with m<1)

Problem of cross-comparison between disciplines

This section was added by myself (T. Rauscher) and is not taken from Hirsch's paper!

It seems highly problematic to use the h-index for cross-comparison between different research disciplines or even subfields within a discipline because the average citation level may be largely different. What counts as a high number of citations in one field, may be seen as an only moderate number in another field. Obviously, this difference is then also reflected in the achievable h-index.

It is important to remember this, especially when comparing two or more individuals regardless of their research area. It is not advised to use the h-index as a measure in such a setting. This may be encountered in comparing candidates for a university faculty position, when the research area of the new faculty member was not well defined in the original advertisement. In such a case, the search committee has to determine the appropriate "citation scale" for the research areas of each candidate separately, before attempting a cross-comparison based on citation numbers (including the h-index).

This makes the h-index an unsuited tool for easy and immediate cross-comparison between research areas.

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